What is the equation of the line parallel to $4x+2y=8$ and passing through the point $(0,1)$? Write the equation in slope-intercept form.
First, subtract $4x$ from both sides and divide by 2 to write the given line in slope intercept form.  This gives $y=-2x+4$.  The slope of this line is $-2$.  So, we need to find a line with a slope of $-2$ that passes through the point $(0,1)$.  Writing this requirement in point-slope form gives the line $y-1=-2x$, or equivalently, $\boxed{y=-2x+1}.$